Solve y=ax^2+bx+y

$$y = a x ^ { 2 } + b x + y$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=-\frac{b}{x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx+y=y$$

Subtract bx from both sides.

$$ax^{2}+y=y-bx$$

Subtract y from both sides.

$$ax^{2}=y-bx-y$$

Combine y and -y to get 0.

$$ax^{2}=-bx$$

The equation is in standard form.

$$x^{2}a=-bx$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=-\frac{bx}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=-\frac{bx}{x^{2}}$$

Divide -bx by x^{2}.

$$a=-\frac{b}{x}$$

Solve for b (complex solution)

$$\left\{\begin{matrix}\\b=-ax\text{, }&\text{unconditionally}\\b\in \mathrm{C}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx+y=y$$

Subtract ax^{2} from both sides.

$$bx+y=y-ax^{2}$$

Subtract y from both sides.

$$bx=y-ax^{2}-y$$

Combine y and -y to get 0.

$$bx=-ax^{2}$$

The equation is in standard form.

$$xb=-ax^{2}$$

Divide both sides by x.

$$\frac{xb}{x}=-\frac{ax^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$b=-\frac{ax^{2}}{x}$$

Divide -ax^{2} by x.

$$b=-ax$$

Solve for a

$$\left\{\begin{matrix}a=-\frac{b}{x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx+y=y$$

Subtract bx from both sides.

$$ax^{2}+y=y-bx$$

Subtract y from both sides.

$$ax^{2}=y-bx-y$$

Combine y and -y to get 0.

$$ax^{2}=-bx$$

The equation is in standard form.

$$x^{2}a=-bx$$

Divide both sides by x^{2}.

$$\frac{x^{2}a}{x^{2}}=-\frac{bx}{x^{2}}$$

Dividing by x^{2} undoes the multiplication by x^{2}.

$$a=-\frac{bx}{x^{2}}$$

Divide -bx by x^{2}.

$$a=-\frac{b}{x}$$

Solve for b

$$\left\{\begin{matrix}\\b=-ax\text{, }&\text{unconditionally}\\b\in \mathrm{R}\text{, }&x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Swap sides so that all variable terms are on the left hand side.

$$ax^{2}+bx+y=y$$

Subtract ax^{2} from both sides.

$$bx+y=y-ax^{2}$$

Subtract y from both sides.

$$bx=y-ax^{2}-y$$

Combine y and -y to get 0.

$$bx=-ax^{2}$$

The equation is in standard form.

$$xb=-ax^{2}$$

Divide both sides by x.

$$\frac{xb}{x}=-\frac{ax^{2}}{x}$$

Dividing by x undoes the multiplication by x.

$$b=-\frac{ax^{2}}{x}$$

Divide -ax^{2} by x.

$$b=-ax$$